My bike starts initially, but the carbs flood very soon thereafter

Gas pouring out the overflow could mean that you've got a particle of something under one of the float needles. It won't flood when not cranking because the vacuum valve in the petcock won't let fuel flow.

Remove the carbs, tip them upside down, remove the float bowl and then each of the floats and needles. Look for something between the needle and its seat. Another possibility is damage to the needle tip.